DNMW04 - New trends and challenges in the mathematics of optimal design

My talk will present some computational design tools targeting various classes of structures and fabrication technologies. In the first half, I will present a method for designing elastic metamaterials that can be fabricated with consumer-level single material 3D printers to achieve custom deformation behaviors. These metamaterials cover a wide range of elastic properties and are optimized for robustness in generic use, experiencing minimal stresses under the worst-case load. Our coarse-scale design optimization can then automatically assign these metamaterials to an input geometry so that the printed object undergoes a user-specified deformation under applied loads. In the second half, I will introduce a new class of deployable elastic gridshell structures. These structures consist of flat, conveniently assembled layouts of elastic beams coupled by rotational joints that can be deployed to programmed 3D curved shapes by a simple expansive actuation. During deployment, the coupling imposed by the joints forces the beams to twist and buckle out of plane, allowing interesting 3D forms to emerge. However the simulation and optimization of these structures is challenging, especially due to the frequent unstable equilibria encountered in the deployment path; I will discuss the efficient algorithms we have developed to assist the design of these structures. This talk is based on joint work with Denis Zorin, Mark Pauly, and Florin Isvoranu.